Rouquier's conjecture on derived equivalence for blocks

Let $F$ be an algebraically closed field of characteristic $p>0$, let $G$ be a finite group, and let $B$ be a block of $FG$ with defect group $D$ and fusion system $\mathcal{F}_D(B)$. Define $Q:=\mathfrak{hyp}(\mathcal{F}_D(B))$, the hyperfocal subgroup of the block fusion system, and let $B_Q$ be the Brauer correspondent of $B$ in $\mathrm{N}_G(Q)$. Rouquier's conjecture. If $Q$ is abelian, then $B$ is derived equivalent to its Brauer correspondent $B_Q$ in $\mathrm{N}_G(Q)$. This is a block-theoretic derived-equivalence conjecture; the source does not state a general resolution.